We compute welfare gains from trade in a dynamic, multicountry model with capital accumulation. We examine transition paths for 93 countries following a permanent, uniform, unanticipated trade liberalization. We develop a gradient-free method to compute the exact transition paths in every country. Relative to a static model, the dynamic welfare gains in a model with balanced trade are three times as large. The gains including transition are 60 percent of those computed by comparing only steady states. Trade imbalances have negligible effects on the cross-country distribution of dynamic gains. However, relative to the balanced-trade model, small, less-developed countries accrue the gains faster in a model with trade imbalances by running trade deficits in the short run but have lower consumption in the long-run. In both models, most of the dynamic gains are driven by capital accumulation.